Paint finishes comprising what are called effect pigments are widespread within the automobile industry. Metallic effect pigments and interference pigments are examples of effect pigments. They endow a paint with additional properties such as changes in lightness and in shade angle-dependently, for example. This means that the lightness or shade of the paint in question changes depending on the angle from which the paint is viewed. Effect pigments result in a visually perceptible granularity or graininess (also called coarseness) and to sparkle effects [“Coloristik für Lackanwendungen (Farbe and Lack Edition)”, Tasso Baurle et al., bound edition—Mar. 14, 2012]. These effects are also referred to as visual texture.
There are currently two techniques in use for characterizing effect paints.
The first technique uses a light source to illuminate a particular paint surface and measures the spectral reflection at different angles. From the results obtained and from the radiation function of the light source it is possible to calculate chromaticity values, e.g., CIEL*a*b* [ASTM E2194 “Standard Test Method for Multiangle Color Measurement of Metal Flake Pigmented Materials”, ASTM E2539 “Standard Test Method for Multiangle Color Measurement of Interference Pigments”].
In the case of the second technique, the paint surface is photographed under defined light conditions and at defined angles. From the images it is then possible to calculate texture parameters which describe the visual texture. Examples of texture parameters are the textural values G diffuse or Gdiff (graininess or coarseness), Si (sparkle intensity), and Sa (sparkle area), as introduced by the company Byk-Gardner [“Beurteilung von Effektlackierungen, Den Gesamtfarbeindruck objektiv messen” (Assessment of effect finishes—objective measurement of overall color impression), Byk-Gardner GmbH, JOT 1.2009, vol. 49, issue 1, pp. 50-52]. The textural values of Byk-Gardner are determined from gray stage images. It is also possible for textural values to be determined individually for different color channels of a color image—e.g., for a red channel, a green channel, and a blue channel.
In a color formula calculation, an attempt is made to reproduce a color original by means of a mixture of available colorants, by calculating the concentrations of colorant required. A necessary precondition in color formula calculation is the prediction of the spectral reflection of a respective color formulation. A color or paint formulation or formula, for the purposes of the present disclosure, refers to a specific composition of different colorants and/or color components with defined respective colorant concentrations. This means that a color or paint formulation defines a kind of list of items—that is, a quantitative composition of a paint comprising its individual components, i.e., its individual color components.
One common method is to calculate reflection spectra on the basis of physical models (e.g., Kubelka-Munk equation). In this process, optical constants are determined for each colorant by means of the physical model, on the basis of actual applications of known colorant compilations. These optical constants are model-dependent and characterize the colorant in question. Examples of the optical constants are the parameters K and S of the Kubelka-Munk equation, which describe the absorption (parameter K) and scattering (parameter S). Where the optical constants are determined for all colorants to be used, the spectral reflection of any desired color formulation can be calculated using the physical model.
For the mixing of a paint, such as a colored paint for a vehicle, for example, it is general practice to use color formulations which indicate a mixing ratio of respective color components to one another in order to generate a paint having a desired color effect. For replication of an effect paint, such as a metallic paint, for example, not only the spectral reflection properties but also objective texture parameters, such as graininess or coarseness, for example, are required as a description of the optical properties of a corresponding shade original.
For the prediction of visual texture parameters of such effect paints on the basis of formula data, as mentioned above, regression-based processes are traditionally used. In such processes, characteristic parameters, such as concentration of pigment types present in a paint, for example, such as of metallic effect pigments and interference pigments, for example, a spectral reflection, predicted by a physical model, or variables derived from respective optical constants of the physical model are calculated for a paint formulation. A linear combination of these parameters then forms a statistical model for the prediction of the visual texture parameters. The coefficients of the linear combination are determined by regression analysis, as described in Kirchner, Ravi “Predicting and measuring the perceived texture of car paints”, Proceedings of the 3rd international conference on Appearance “Predicting Perceptions”, Edinburgh, Apr. 17-19, 2012.
Another way of predicting the visual texture parameters of an effect finish is by using artificial neural networks.
One neural network for use in this context is based on a learning process referred to as backpropagation. The neurons of the neural network are arranged in layers. These include a layer with input neurons (input layer), a layer with output neurons (output layer), and one or more inner layers. The output neurons are the visual texture parameters of the paint formulation that are to be predicted, in other words the aforementioned parameters of Si, Sa, and Gdiff.
To predict the spectral reflection of an effect paint formulation, as already mentioned, a physical model is used.
In a first known solution approach, input parameters or input neurons used for the neural network are the concentrations of the colorants or color components used in the particular paint formulation under consideration, and the reflection spectrum as predicted by a physical model.
The use as input parameters of concentrations of colorants to be employed has a number of disadvantages, however:                The number of colorants in a paint series is very high, and so the number of neurons in the input layer of the neural network is very large. Precise prediction of the texture parameters requires a large quantity of training data.        In the event of any change in the paint series, the neural network must be redefined, retrained, and retested. This implies considerable administration effort and expense.        The effort and expense of adding a further colorant to a paint series is great: in the case of new colorants, numerous mixtures must be produced as a basis for training the neural network.        
Known from the U.S. Pat. No. 6,714,924 B1 is a method and apparatus for color matching wherein neural networks are employed. Here, the color of a color standard is expressed by color values, with the input signals of the neural network used being related to paint bases. Furthermore, weighted connections are provided between the input nodes of the input layer of the neural network and the output nodes of the output layer of the neural network. Initial weighted connections here determine the respective contribution of the paint bases of the input layer to each output color component.
Known from US 2009/0157212 A1 is a method and a system for determining a paint formulation comprising an effect pigment. The system comprises a roughness measuring instrument which must be placed adjacent to the painted surface, such as that of a vehicle, for example, with a technician comparing the display with the painted surface in order to determine the roughness of the effect pigment.